Dirichlet conditions

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Dirichlet conditions guarantee that a periodic function can be exactly represented by its Fourier transform.



Condition 1[edit]

The function must be absolutely integrable over a single period . This is equivalent to the statement that the area enclosed between the abcissa and the function is finite over a single period.

Condition 2[edit]

Given any finite period of time the number of local maxima and minima of within that period is finite.

Condition 3[edit]

Given any finite period of time there is a finite number of discontinuities in the function